Stochastic differential games: the potential approach. Issue 7 (2nd October 2020)

• Record Type: Journal Article
• Authors: Fonseca-Morales, A.; Hernández-Lerma, O.
• Is Part Of: Stochastics. Volume 92:Issue 7(2020)
• Page Start: 1125
• Page End: 1138
• Publication Date: 2020-10-02
• Subjects: Stochastic differential games -- Nash equilibria -- potential games -- optimal control -- maximum principle; 91A23 -- 91A25 -- 49N70 -- 93E20 -- 91A10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1691208
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : A noncooperative stochastic differential game (SDG) is said to be a potential game if there exists an associated stochastic control problem whose optimal solutions are Nash equilibria for the given game. In this paper, we give sufficient conditions for an SDG to be a potential game. To this end, our main tools are suitable versions of the stochastic maximum principle. Our results are illustrated with several examples, including team games and separable games, which have Pareto-optimal Nash equilibria.